- Radical of an integer
In
mathematics , the radical of a positiveinteger "n" is defined as the product of theprime number s dividing "n"::
For example,
:
The radical of any integer "n" is the largest square-free divisor of "n".
Radical numbers for the first few positive integers are 1, 2, 3, 2, 5, 6, 7, 2, 3, 10, ... (sequence [http://www.research.att.com/~njas/sequences/A007947 A007947] in
OEIS ).The function is multiplicative.
One of the most striking applications of the notion of radical occurs in the
abc conjecture , which states that, for any "ε" > 0, there exists a finite "Kε" such that, for all triples ofcoprime positive integers "a", "b", and "c" satisfying "a" + "b" = "c",:
References
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